Ignoring settlement for a moment I see three states - installed (W but W+P1 would work in most cases), operating #1 (W+T1+P1) and operating #2 (W+T2+P1). CAESAR II would recommend two expansion stress ranges: (Operating #1 - Installed) and (Operating #2 - Installed). It would your responsibility to create a third range: (Operating #1 - Operating #2). That might be the worst case here since T1 and T2 straddle ambient temperature.
Now add the settlement.
If settlement occurs immediately after the system goes into service, I suggest there are four states - installed (W or W+P1, as above), installed with settlement (W+D1)and the two operating cases (W+T1+P1+D1)(W+T1+P1+D1). Range calculations might then be between installed and installed with settlement; the two operating cases with settlement and the installed with settlement; and also between the two operating cases with settlement. If settlement is slow then the original two operating cases come into play. You should consider all these positions when you are looking for the maximum expansion stress range. Perhaps you can eliminate some of the ranges but you should consider all of these cases in your "State #1 - State #2" evaluation.
Most users stop there but to follow the Code you should include the damage of lesser stress range cycles in setting the number of cycles used in the allowable stress range calculation for that highest stress range.
Things are simpler for linear systems.

I see no distinction between pipe strain caused by settlement and that caused by thermal pipe strain - as you imply.